Neanderthal-human Hybrids

Evidence from studies of nuclear and mitochondrial DNA extracted from Neanderthal fossils and humans points to fascinating hypotheses concerning the types of interbreeding that occurred between these two species. Humans and Neanderthals share a small percentage of nuclear DNA. However, humans and Neanderthals do not possess the same mito­chondrial DNA. In mammals, mitochondrial DNA is exclusively maternally inherited. Taking into account an understanding of interspecific hybridity, the available data leads to the hypothesis that only male Neanderthals were able to mate with female humans. If Haldane’s Law applied to the progeny of Neanderthals and humans, then female hybrids would survive, but male hybrids would be absent, rare, or sterile. Interbreeding between male Neanderthals and female humans, as the only possible scenario, accounts for the presence of Neanderthal nuclear DNA, the scarcity of Neanderthal Y-linked genes, and the lack of mitochondrial DNA in modern human populations.

Very flawed indeed. Broad/bad generalizations about what mt-DNA tells about ancestry.
Aditionally, is something really weird at title: …”Human-Neanderthals”…???
Neandertal are humans too, by all means.

First – Neanderthals are not always considered humans. They can be classed as a separate species (Homo neanderthalensis) or as a race (sub species: Homo sapiens neanderthalensis) of Homo sapiens. Either way, they are not Homo sapiens proper.

Second, modern human is a hybrid of neanderthal and Homo sapiens. This is known because we share their nuclear (genomic) DNA.

With that out of the way, we can go back to the importance of mtDNA (mitochondrial DNA):

mtDNA in sperm is destroyed upon implantation with the egg. Therefore, mtDNA is only past to offspring from the mother. As a result of this, in order to have mtDNA in neanderthal-human hybrids, male Homo sapiens would have had to have bread with female neanderthals (and offspring would have had to have been fertile).

Moreover, our mtDNA has to have to come from somewhere. According to the evidence, it only came from Homo sapiens.

Thus, offspring from Neanderthal (female) and human (male) crossings were not fertile, OR just didn’t happen.